MODULE TikTak_mod

   USE Parameters, ONLY: procid, OutputDir
   USE amoeba_mod, ONLY: amoeba

   IMPLICIT NONE

   INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(15, 307)
   REAL(dp) :: dummy_dp
   REAL(dp), PARAMETER :: positiveInf = HUGE(dummy_dp)

CONTAINS

   SUBROUTINE TikTak(restart, fn, J, lb, ub, step_nm, N_start, perc_local, tol_nm, iter_nm, seq_weight, xopt, fopt, &
                     no_weight, obj_tol, jmin)

      IMPLICIT NONE

      ! Arguments
      INTEGER, INTENT(IN) :: restart ! = 0 to start from scratch, = 1 to restart from local optimization loop
      REAL(dp), EXTERNAL :: fn ! function to be minimized
      INTEGER, INTENT(IN) :: J ! dimension of parameter vector
      REAL(dp), INTENT(IN) :: lb(J), ub(J) ! bounds on parameter vector
      REAL(dp), INTENT(IN) :: step_nm(J) ! step size in Nelder-Mead local optimizations
      INTEGER, INTENT(IN) :: N_start ! number of Halton points to solve model at initially
      REAL(dp), INTENT(IN) :: perc_local ! top percent of N_start points to consider as candidates
      REAL(dp), INTENT(IN) :: tol_nm ! tolerance for Nelder-Mead
      INTEGER, INTENT(IN) :: iter_nm ! maximum number of iterations for Nelder-Mead
      LOGICAL, INTENT(IN) :: seq_weight ! whether to do 2-stage local optimizations
      REAL(dp), INTENT(OUT) :: xopt(J), fopt ! optimization point and objective function value
      ! Optional arguments
      LOGICAL, INTENT(IN), OPTIONAL :: no_weight ! if seq_weight = .FALSE., whether to turn off weighting across points
      REAL(dp), INTENT(IN), OPTIONAL :: obj_tol ! tolerance for objective function: if present you round
      INTEGER, INTENT(IN), OPTIONAL :: jmin ! parameter to sort by if you have ties in objective function

      ! For program
      REAL(dp), ALLOCATABLE :: results(:, :), top_haltons(:, :)
      REAL(dp) :: start(J), theta_i
      INTEGER :: i, N_top, flag, iStart, LOCALSTAGE, N_STAGES, STAGE
      LOGICAL :: WEIGHT

      ! Number of Halton points from which you'll run NM
      N_top = ceiling(N_start*perc_local)

      ! Calculate number of local stages
      N_STAGES = 1
      IF (seq_weight) N_STAGES = 2

      ! Determine whether to use weighting
      IF (PRESENT(no_weight) .and. N_STAGES .eq. 1) THEN
         WEIGHT = .NOT. no_weight
      ELSE
         WEIGHT = .TRUE.
      END IF

      IF (restart .eq. 0) THEN
         ! Generate Halton sequences
         ALLOCATE (results(N_start, J + 1))
         results = positiveInf
         CALL generate_haltons(N_start, J, lb, ub, results(:, 1:J))
         ! Evaluate at each Halton point
         DO i = 1, N_start
            results(i, J + 1) = fn(results(i, 1:J))
         END DO
         IF (procid .eq. 0) PRINT *, "FINISHED EVALUATION AT HALTON POINTS"
         ! Keep top perc_col*N_start Halton points
         ALLOCATE (top_haltons(N_top, J + 1))
         CALL sort_array_by(results, J + 1)
         top_haltons = results(1:N_top, :)
         DEALLOCATE (results)
         ! Initialize before local optimization loop
         ALLOCATE (results(N_top, J + 2)) ! store parameters, function results, and NM flags
         results = 0d0
         results(:, 1:J + 1) = top_haltons
         DEALLOCATE (top_haltons)
         fopt = positiveInf
         xopt = 0d0
         iStart = 1
         LOCALSTAGE = 1
      ELSE
         ! Read in results for restart
         ALLOCATE (results(N_top, J + 2))
         OPEN (9361, FORM='unformatted', FILE=trim(OutputDir)//'TikTak_status')
         READ (9361) results, fopt, xopt, iStart, LOCALSTAGE
         CLOSE (9361)
         IF (iStart > N_top) THEN
            iStart = 1
            LOCALSTAGE = N_STAGES
         END IF
         IF (procid .eq. 0) PRINT *, "RESTARTING TIKTAK AT ITERATION", iStart, "OF", N_top
         IF (procid .eq. 0) PRINT *, " LOCAL STAGE", LOCALSTAGE, "OF", N_STAGES
      END IF

      ! Loop through best points performing local optimizations
      DO STAGE = LOCALSTAGE, N_STAGES
         DO i = iStart, N_top
            IF (procid .eq. 0) PRINT *, "STARTING LOCAL OPTIMIZATION", i, "OF", N_top
            IF (procid .eq. 0) PRINT *, " LOCAL STAGE", STAGE, "OF", N_STAGES
            start = results(i, 1:J)
            IF (i > 1 .and. (STAGE > 1 .or. N_STAGES .eq. 1) .and. WEIGHT) THEN
               theta_i = MIN(MAX(0.1d0, SQRT(real(i, kind=dp)/real(N_top, kind=dp))), 0.995d0)
               start = theta_i*xopt + (1d0 - theta_i)*start
            END IF
            CALL amoeba(J, start, results(i, 1:J), results(i, J + 1), fn, step_nm, tol_nm, iter_nm, flag)
            results(i, J + 2) = real(flag, kind=dp)
            IF (results(i, J + 1) < fopt) THEN
               fopt = results(i, J + 1)
               xopt = results(i, 1:J)
            END IF
            ! Output results for possible restart
            IF (procid .eq. 0) THEN
               OPEN (9361, FORM='unformatted', FILE=trim(OutputDir)//'TikTak_status')
               WRITE (9361) results, fopt, xopt, i + 1, STAGE
               CLOSE (9361)
            END IF
         END DO
         iStart = 1
      END DO

      ! Write out results with flags
      IF (procid .eq. 0) CALL WriteMatrix2d_realdp(trim(OutputDir)//'TikTak_results.txt', 9361, results)

      ! Return minimum value of parameter in index jmin that achieves maximum rounded objective function, if requested
      IF (PRESENT(obj_tol) .and. PRESENT(jmin)) THEN
         CALL sort_array_by(results, J + 1)
         DO i = 1, N_top
            IF (results(i, J + 1) - results(1, J + 1) > obj_tol) EXIT
            IF (results(i, jmin) < xopt(jmin)) xopt = results(i, 1:J)
         END DO
      END IF

      ! Deallocate
      DEALLOCATE (results)

   END SUBROUTINE TikTak

   ! Routine to sort an array by a column
   SUBROUTINE sort_array_by(array, bycol)
      REAL(dp), INTENT(INOUT) :: array(:, :)
      INTEGER, INTENT(IN) :: bycol
      INTEGER :: irow, krow, nrow, ncol
      REAL(dp), ALLOCATABLE :: buf(:)
      nrow = size(array, 1)
      ncol = size(array, 2)
      ALLOCATE (buf(ncol))
      DO irow = 1, nrow
         krow = minloc(array(irow:nrow, bycol), dim=1) + irow - 1
         buf = array(irow, :)
         array(irow, :) = array(krow, :)
         array(krow, :) = buf(:)
      END DO
      DEALLOCATE (buf)
   END SUBROUTINE sort_array_by

   ! Function for rounding x to nearest multiple of mult
   REAL(dp) FUNCTION custom_round(x, mult)
      IMPLICIT NONE
      REAL(dp), INTENT(IN) :: x, mult
      custom_round = mult*REAL(FLOOR(x/mult), kind=dp)
   END FUNCTION custom_round

   ! Routine to write out 2D dp matrix
   SUBROUTINE WriteMatrix2d_realdp(f, nfile, mat)
      CHARACTER(len=*), INTENT(IN) :: f
      INTEGER, INTENT(IN) :: nfile
      REAL(dp), INTENT(in) :: mat(:, :)
      CHARACTER :: lstring*80
      INTEGER :: i1, n1, n2
      n1 = size(mat, 1)
      n2 = size(mat, 2)
      OPEN (nfile, FILE=f, STATUS='replace')
      WRITE (UNIT=lstring, FMT='(I5)') n2
      lstring = '('//trim(lstring)//'F24.15)'
      DO i1 = 1, n1
         WRITE (nfile, lstring) (mat(i1, :))
      END DO
      CLOSE (nfile)
   END SUBROUTINE WriteMatrix2d_realdp

   ! Routine written by Tim to generate an array of Halton sequences covering the parameter
   ! space from lower to upper bound
   SUBROUTINE generate_haltons(N, J, lb, ub, x)
      IMPLICIT NONE
      INTEGER, INTENT(IN) :: N, J ! number of points and dimension of parameter space
      REAL(dp), INTENT(IN) :: lb(J), ub(J) ! lower and upper bounds
      REAL(dp), INTENT(OUT) :: x(N, J) ! Output
      INTEGER :: iH, iJ
      REAL(dp) :: hx(J)
      DO iH = 1, N
         CALL halton(iH, J, hx)
         DO iJ = 1, J
            x(iH, iJ) = lb(iJ) + hx(iJ)*(ub(iJ) - lb(iJ))
         END DO
      END DO
   END SUBROUTINE generate_haltons

   SUBROUTINE halton(i, m, r)

      !*****************************************************************************80
      !
      ! HALTON computes an element of a Halton sequence.
      !
      !  Licensing:
      !
      !    This code is distributed under the GNU LGPL license.
      !
      !  Modified:
      !
      !    10 August 2016
      !
      !  Author:
      !
      !    John Burkardt
      !
      !  Reference:
      !
      !    John Halton,
      !    On the efficiency of certain quasi-random sequences of points
      !    in evaluating multi-dimensional integrals,
      !    Numerische Mathematik,
      !    Volume 2, pages 84-90, 1960.
      !
      !  Parameters:
      !
      !    Input, INTEGER ::  I, the index of the element of the sequence.
      !    0 <= I.
      !
      !    Input, INTEGER ::  M, the spatial dimension.
      !    1 <= M <= 100.
      !
      !    Output, REAL(dp) :: R(M), the element of the sequence with index I.
      !
      IMPLICIT NONE

      INTEGER, INTENT(IN) ::  i
      INTEGER, INTENT(IN) ::  m
      REAL(dp), INTENT(OUT) :: r(m)

      INTEGER ::  d
      INTEGER ::  i1
      INTEGER ::  j
      REAL(dp) :: prime_inv(m)
      INTEGER ::  t(m)

      t(1:m) = abs(i)
      !
      !  Carry out the computation.
      !
      DO i1 = 1, m
         prime_inv(i1) = 1.0d0/real(prime(i1), kind=dp)
      END DO

      r(1:m) = 0.0d0

      DO WHILE (any(t(1:m) /= 0))
         DO j = 1, m
            d = mod(t(j), prime(j))
            r(j) = r(j) + real(d, kind=dp)*prime_inv(j)
            prime_inv(j) = prime_inv(j)/real(prime(j), kind=dp)
            t(j) = (t(j)/prime(j))
         END DO
      END DO

   END SUBROUTINE halton

   INTEGER FUNCTION prime(n)

      !*****************************************************************************80
      !
      ! PRIME returns any of the first PRIME_MAX prime numbers.
      !
      !  Discussion:
      !
      !    PRIME_MAX is 1600, and the largest prime stored is 13499.
      !
      !    Thanks to Bart Vandewoestyne for pointing out a typo, 18 February 2005.
      !
      !  Licensing:
      !
      !    This code is distributed under the GNU LGPL license.
      !
      !  Modified:
      !
      !    18 February 2005
      !
      !  Author:
      !
      !    John Burkardt
      !
      !  Reference:
      !
      !    Milton Abramowitz, Irene Stegun,
      !    Handbook of Mathematical Functions,
      !    US Department of Commerce, 1964, pages 870-873.
      !
      !    Daniel Zwillinger,
      !    CRC Standard Mathematical Tables and Formulae,
      !    30th Edition,
      !    CRC Press, 1996, pages 95-98.
      !
      !  Parameters:
      !
      !    Input, INTEGER ::  N, the index of the desired prime number.
      !    In general, is should be true that 0 <= N <= PRIME_MAX.
      !    N = -1 returns PRIME_MAX, the index of the largest prime available.
      !    N = 0 is legal, returning PRIME = 1.
      !
      !    Output, INTEGER ::  PRIME, the N-th prime.  If N is out of range,
      !    PRIME is returned as -1.
      !
      IMPLICIT NONE

      INTEGER, PARAMETER :: prime_max = 1600

      INTEGER, SAVE :: icall = 0
      INTEGER ::  n
      INTEGER, SAVE, DIMENSION(prime_max) :: npvec

      IF (icall == 0) THEN

         icall = 1

         npvec(1:100) = (/ &
                        2, 3, 5, 7, 11, 13, 17, 19, 23, 29, &
                        31, 37, 41, 43, 47, 53, 59, 61, 67, 71, &
                        73, 79, 83, 89, 97, 101, 103, 107, 109, 113, &
                        127, 131, 137, 139, 149, 151, 157, 163, 167, 173, &
                        179, 181, 191, 193, 197, 199, 211, 223, 227, 229, &
                        233, 239, 241, 251, 257, 263, 269, 271, 277, 281, &
                        283, 293, 307, 311, 313, 317, 331, 337, 347, 349, &
                        353, 359, 367, 373, 379, 383, 389, 397, 401, 409, &
                        419, 421, 431, 433, 439, 443, 449, 457, 461, 463, &
                        467, 479, 487, 491, 499, 503, 509, 521, 523, 541/)

         npvec(101:200) = (/ &
                          547, 557, 563, 569, 571, 577, 587, 593, 599, 601, &
                          607, 613, 617, 619, 631, 641, 643, 647, 653, 659, &
                          661, 673, 677, 683, 691, 701, 709, 719, 727, 733, &
                          739, 743, 751, 757, 761, 769, 773, 787, 797, 809, &
                          811, 821, 823, 827, 829, 839, 853, 857, 859, 863, &
                          877, 881, 883, 887, 907, 911, 919, 929, 937, 941, &
                          947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, &
                          1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, &
                          1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, &
                          1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223/)

         npvec(201:300) = (/ &
                          1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, &
                          1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, &
                          1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, &
                          1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, &
                          1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, &
                          1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, &
                          1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, &
                          1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, &
                          1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, &
                          1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987/)

         npvec(301:400) = (/ &
                          1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, &
                          2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, &
                          2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, &
                          2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, &
                          2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, &
                          2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, &
                          2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, &
                          2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, &
                          2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, &
                          2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741/)

         npvec(401:500) = (/ &
                          2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, &
                          2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, &
                          2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, &
                          3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, &
                          3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, &
                          3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, &
                          3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, &
                          3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, &
                          3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, &
                          3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571/)

         npvec(501:600) = (/ &
                          3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, &
                          3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, &
                          3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, &
                          3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, &
                          3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, &
                          4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, &
                          4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, &
                          4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, &
                          4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, &
                          4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409/)

         npvec(601:700) = (/ &
                          4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, &
                          4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, &
                          4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, &
                          4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, &
                          4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, &
                          4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, &
                          4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, &
                          5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, &
                          5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, &
                          5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279/)

         npvec(701:800) = (/ &
                          5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, &
                          5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, &
                          5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, &
                          5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, &
                          5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, &
                          5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, &
                          5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, &
                          5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, &
                          5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, &
                          6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133/)

         npvec(801:900) = (/ &
                          6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, &
                          6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, &
                          6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, &
                          6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, &
                          6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, &
                          6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, &
                          6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, &
                          6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, &
                          6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, &
                          6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997/)

         npvec(901:1000) = (/ &
                           7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, &
                           7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, &
                           7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, &
                           7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, &
                           7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, &
                           7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, &
                           7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, &
                           7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, &
                           7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, &
                           7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919/)

         npvec(1001:1100) = (/ &
                            7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, &
                            8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, &
                            8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, &
                            8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, &
                            8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, &
                            8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, &
                            8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, &
                            8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, &
                            8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, &
                            8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831/)

         npvec(1101:1200) = (/ &
                            8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, &
                            8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, &
                            9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, &
                            9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, &
                            9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, &
                            9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, &
                            9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, &
                            9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, &
                            9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, &
                            9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733/)

         npvec(1201:1300) = (/ &
                            9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, &
                            9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, &
                            9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007, &
                            10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, &
                            10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, &
                            10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271, &
                            10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337, 10343, &
                            10357, 10369, 10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459, &
                            10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531, 10559, 10567, &
                            10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, 10651, 10657/)

         npvec(1301:1400) = (/ &
                            10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, 10739, &
                            10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, &
                            10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, &
                            10957, 10973, 10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, &
                            11069, 11071, 11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149, &
                            11159, 11161, 11171, 11173, 11177, 11197, 11213, 11239, 11243, 11251, &
                            11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 11329, &
                            11351, 11353, 11369, 11383, 11393, 11399, 11411, 11423, 11437, 11443, &
                            11447, 11467, 11471, 11483, 11489, 11491, 11497, 11503, 11519, 11527, &
                            11549, 11551, 11579, 11587, 11593, 11597, 11617, 11621, 11633, 11657/)

         npvec(1401:1500) = (/ &
                            11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, 11743, 11777, &
                            11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833, &
                            11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, &
                            11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, &
                            12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, &
                            12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, &
                            12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277, 12281, 12289, &
                            12301, 12323, 12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401, &
                            12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 12487, &
                            12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553/)

         npvec(1501:1600) = (/ &
                            12569, 12577, 12583, 12589, 12601, 12611, 12613, 12619, 12637, 12641, &
                            12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, 12721, 12739, &
                            12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829, &
                            12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, &
                            12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, &
                            13009, 13033, 13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, &
                            13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177, 13183, 13187, &
                            13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309, &
                            13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397, 13399, 13411, &
                            13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499/)

      END IF

      IF (n == -1) THEN
         prime = prime_max
      ELSE IF (n == 0) THEN
         prime = 1
      ELSE IF (n <= prime_max) THEN
         prime = npvec(n)
      ELSE
         prime = -1
         WRITE (*, '(a)') ' '
         WRITE (*, '(a)') 'PRIME - Fatal error!'
         WRITE (*, '(a,i8)') '  Illegal prime index N = ', n
         WRITE (*, '(a,i8)') '  N should be between 1 and PRIME_MAX =', prime_max
         STOP 1
      END IF

   END FUNCTION prime

END MODULE TikTak_mod
